I have a situation where the only proprietary charging device I have for 12 volt cellphone is a UK unit rated at 220v 50 cycle input.

I need to charge the phone here in Canada, and have obtained the necessary outlet adaptor to plug the UK square pin plug in to a standard 110volt 60cycle north american wallsocket. The charging bar on the phone indicates that it is accepting a charge. Am I doing any harm by attempting to charge the device at half the rated input requirement, or am I simply slowing down the rate of charge?

Well, if you were going to let the smoke out, you would have by now!
You will however be doing more (or should I say less??) then reducing the "rate of charge" you are also reducing the charging voltage. Basically your batter is being charged, but not fully. You will probably notice shorter battery life out of a charge. The output of a transformer is proportional to it's input.

If you really cannot find a 110VAC charger for it, can you find a 12VDC car charger for it? Or you could also buy a converter to convert 110 to 220 for about 50 bucks, give or take...

If you have access to a multimeter/voltmeter of some sort, measure the voltage put out by the charger while running off 110VAC. If there are a million pins and you can't figure out which ones to measure off of, just charge the battery then measure the batteries voltage, that will be a close enough measurement to what the charger is putting out under the load of charging.

I do have the necessary equipment to do the tests you suggest, so I have a project for the weekend. I also have a huge 110 to 220 step up transformer, but I was trying to be lean on the equipment side for when we travel. The phone is actually for my wife. Unfortunately it is a Seimens model not supported here in Canada, otherwise the car charger would have been my first thought. Thanks again for taking the trouble to respond.

LOL,
Yeah, use the step up at home, and the other method when traveling! Good idea. I was just thinking, by the time you bought all the converters (if you didn't have the one you have already) it probably would be cheaper to just buy a new phone!
Well, good luck. Like I said, you are fine to use it, the only thing is it will probably have less run time per charge, but if it works, it works!
Good luck.

You are right about the phone cost, but this is my wife's pet portable (it has a cute little detachable camera - go figure). However, the big transformer came with me from the UK thirty years ago (hence the size) and the small wall socket adaptor cost CDN$15, so the entry fee has been tolerable.

My multimeter doesn't register direct voltage ratings as such, but it does have VDC settings in increments, one of which is 10v. I tested the current across the ouput terminals of the charger and it registered high in the green band ("good") at 5 ohms (?) Jeez, I used to know all this stuff back in my ham radio days, but now I am losing it. So perhaps this is enough to charge the phone battery OK. It certainly seemed to do the trick.

My guess is that this is one of those dual voltage chargers anyway and they just don't label them as such in the UK. Most of the ones we use here at work (we develop content for cellular devices) seem to be rated 110/220, and I can't see Siemens being more sophisticated than to buy the most readily available chinese gizmos and simply stick their own plug on the end. Who knows?